Example 05.08 Activity Coefficient of the Monomer in a Polymer Using the Athermal

Flory-Huggins Equation

problem:

Calculate the activity coefficient of the monomer in a polymer using the athermal Flory-Huggins equation. For the calculation the following volumes should be used:

v_{1} = 70 cm^{3}/mol v_{2} = 70000 cm^{3}/mol

general

constants

and

definitions:

input data

Liquid molar volumes of the components

Solution

Using equation 5.33, the activity coefficient can be calculated from the volume fractions q of the components in the mixture:

For the activity coefficient, the following expression results:

The surface fraction vector is calculated from the mole fraction vector via:

Simplification of the expression for the activity coefficient leads to:

To avoid the singularity at the pure components, the following function V should be used, which provides identical values without the singularity.

Calculation should be performed for a monomer mole fraction of 0.2:

This results in the following volume fractions:

The following values for the activity coefficients can be found:

The same function can now be used to plot the activity coefficients as function of composition:

Or in logarithmic form:

Plotting the logarithm of the ratio of the activity coefficients as function of concentration leads to:

The curvature above is very typically for strongly assymetric systems with negative deviation from Raoult's Law.